President-elect Donald J. Trump boasted throughout the presidential campaign of his loyalty as a singular quality. “Folks, look, I’m a loyal person,” Mr. Trump said at a CNN town hall in April, explaining why he would not rid his campaign of a staff member who was under fire.

Loyalty appears to be paramount for Mr. Trump, until it isn’t.

Some of Mr. Trump's earliest supporters — among them Rudolph W. Giuliani, Gov. Chris Christie of New Jersey, Sarah Palin, Newt Gingrich and Mike Huckabee — have not fared well in the job sweepstakes. On top of that, they have been left in the December cold while Mitt Romney, a leader of the “never Trump” movement, has been wooed by the president-elect’s advisers for secretary of state.

“It kind of reminds me of the Reagan administration,” said Roger Stone, a long-serving informal adviser to Mr. Trump who met with him at Trump Tower last week. “We used to have a running joke where it was news if somebody who supported Reagan got a job.”

Mr. Trump put out a face-saving statement on Mr. Giuliani’s behalf on Friday, saying that the former mayor of New York had withdrawn from contention for secretary of state — the only job he had wanted.

Trump advisers say there are a variety of reasons that Mr. Trump has turned his back on many loyalists. Some brought too much personal baggage, like Mr. Giuliani, with his paid speeches to a group that was once on the State Department’s list of terrorist organizations, or Mr. Christie, who is considered deeply problematic by Mr. Trump’s circle because of the George Washington Bridge lane-closing scandal.

Others were rejected by new gatekeepers around Mr. Trump, most prominently Reince Priebus, Mr. Trump’s incoming White House chief of staff, the departing chairman of the Republican National Committee and the man who has almost a lock on hiring for West Wing staff and cabinet posts, and Stephen K. Bannon, Mr. Trump’s chief strategist for the White House. They have worked jointly on personnel decisions, with just a few additional advisers.

In the case of Mr. Giuliani and Mr. Christie — who defended Mr. Trump more forcefully than many other surrogates — both men were repeatedly left languishing in the face of media reports about how Mr. Trump viewed them. Mr. Giuliani withdrew his name from contention on Nov. 29, according to Mr. Trump’s statement.

Gov. Chris Christie of New Jersey wanted to be attorney general, but turned down a White House advisory role when offered.

Mr. Trump’s allies point out that both men were offered other positions, just not the specific ones they wanted. Mr. Giuliani, for instance, was offered three other jobs, including attorney general — the job that Mr. Christie had wanted. Instead, Mr. Trump offered Mr. Christie a White House advisory role, which he declined.

Mr. Gingrich, the former House speaker and an early supporter, has taken his rejection, at least publicly, with magnanimity. Mr. Gingrich decided to withdraw his name from consideration for a cabinet post early on, and took a broad advisory role. Mr. Trump, he said, has “an obligation to the mission and the assignment that transcends the people who came with” him in the campaign.

Mr. Gingrich said he expected that Mr. Trump would be “tough-minded about whether the person is capable of doing the job.”

He added, “There are things that work in campaigns that may or may not work in government.”

There are potential staff picks who some Trump loyalists believe deserve a role. Among them is Laura Ingraham, the conservative radio host and vocal booster of Mr. Trump who some supporters had hoped would become his press secretary.

Ms. Ingraham was only recently brought in for an interview and is not seen as likely to get the job, which is expected to go to Sean Spicer, who was recently the lead spokesman under Mr. Priebus at the Republican National Committee.

Mr. Trump is said to be focused primarily on cabinet-level jobs, and has given little thought to lower-level staffing decisions and state-level campaign aides who worked aggressively for him. Still, Mr. Trump has been less than pleased in recent days with stories about long-serving staff and supporters who have not been contacted by anyone at Trump Tower. So Mr. Priebus, over the last 48 hours, has begun reaching out in earnest to some of those people.

“I don’t think he’s saying, ‘I’m not going to take care of my loyal friends,’” said Christopher Ruddy, of the conservative website Newsmax, who is a friend of Mr. Trump’s. “I think all of those people will be rewarded, it’s just taking time.”

Mr. Priebus, whom Mr. Trump rewarded with one of the most powerful jobs in Washington, was often a public loyalist during some of the lowest points of Mr. Trump’s campaign. But he is viewed skeptically by some people around Mr. Trump who recall bitterly the clashes between the campaign and the party committee at various points during the race.

Newt Gingrich, the former House Speaker, and his wife Callista met last month with the transition team at Trump Tower.

Mr. Priebus’s detractors have pointed to his frequent private criticism of Mr. Trump to other Republicans throughout the presidential race, including his blunt and discouraging remarks after a recording emerged of Mr. Trump boasting about grabbing women by their genitals. Mr. Priebus and his committee strongly indicated to allies shortly before the election that they believed Mr. Trump would lose.

It is “premature” to judge all of the choices, said Mr. Stone, given that the White House staff has not been named beyond Mr. Priebus; the White House counsel, Don McGahn; and Mr. Bannon. But he added that if the staff is primarily “cronies” of Mr. Priebus from the party committee, it could be a problem. He said that the president’s spokesman, the face of the administration, should be a long-term supporter.

Others remember how Representative Cathy McMorris Rodgers, Republican of Washington, spoke this past March about Mr. Trump’s history of demeaning comments about women.

“I think they are hurtful to the party, a party that has been founded on equal opportunity for all,” she said at the time.

Yet Ms. McMorris Rodgers has emerged as the likely choice to be Mr. Trump’s secretary of the interior, while loyalists who backed the president-elect early on have withered on the vine of the transition process.